note explains the following topics: Subtraction, Division,
Elimination by comparison, General rule for extracting any root of a
polynomial, Multiplication and division of surds, First and second rule for
quadratic equations, Properties of the roots of quadratic equations,
Binomial and multinomial Theorem demonstrated, Summation ofin&
This note explains the
following topics: Group Theory, Sylow’s Theorem, Field and Galois Theory,
Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring
Structure Theory, Tensor Products.
This book is intended as a sequel to
our Elementary Algebra for Schools. The first few chapters are devoted to a
fuller discussion of Ratio, Proportion, Variation, and the Progressions, and
then introduced theorems with examples.
Sinclair Hall, Samuel Ratcliff Knight
explains the following topics: Groups, The Sylow theorems, The Jordan-Holder
theorem and solvable groups, Free groups and free products, Modules,
Localization of rings and modules, Free modules and rank, Infinite Galois
theory, Cyclotomic fields, Kummer Theory , Cyclic Galois extensions,
Calculation of Galois groups.
note covers the following topics: The symmetric monoidal
category nCob and nTFTs, Duality in monoidal categories, Presentation of 1Cob by
generators and relations, 2TFTs and Frobenius algebra, Extending down TFTs,
Bicategories, Symmetric monoidal bicategories, Symmetric monoidal structures on
note covers the following topics: Disintegration and Assembly, Associative
Algebras and Their Modules, Algebras and Modules over alpha operads, Little
Cubes and Factorizable Sheaves, Algebraic Structures on alpha Categories,
Algebra in the Stable Homotopy Category.
This note covers the following topics: group theory and graphs with
large girth, expanders and superconcentrators, character sums and
pseudo-random graphs, real varieties and sign patterns of polynomials, The
Chevalley-Warning theorem, Abelian groups and regular graphs, hyperbolic
geometry and triangulations of polytopes and polygons, the Erdos-Mozer
conjecture and the hard Lefschetz theorem.
These notes are designed for students who have done very little
mathematics in high school and, in particular, have never done any calculus.
Topics covered includes: Real Numbers, Inequalities and Absolute Values,
Arithmetic and Geometric Series, Probability and the Binomial Theorem, Logs and
Exponentials, Trigonometric Functions, Complex Numbers, Polynomials and Systems
of Linear Equations.